Angelo Rizzieri

01 Research

1. Billiards, Dynamics, and Geometry

   Work in progress

   REU in Topological Dynamical Systems, advised by Dr. Tina Torkaman, with Charlotte Zelin, Summer 2026

   An expository paper on billiards in the circle, the torus, and polygonal tables. We show an orbit in the circle is periodic exactly when the reflection angle is a rational multiple of 2π, and dense otherwise by Kronecker's theorem. On the torus we use Weyl equidistribution to prove a trajectory of irrational slope meets a region in proportion to its area. We then code trajectories as infinite words, prove the Morse-Hedlund classification, and show an irrational slope gives complexity k+1, so the coding is Sturmian. The last sections construct translation surfaces from polygons glued in parallel pairs, define the SL(2,R) action and the Veech group, and take up the illumination problem following Hubert, Schmoll, and Troubetzkoy.

2. Feasibility Bound for the Invariant-Based Rank-1 OCRS in the Adversarial Order Model

   Algorithmic Game Theory, advised by Dr. Ishan Agarwal, August 2025

   An online contention resolution scheme decides item by item, and permanently, whether to accept what arrives. I proved that in the rank 1 matroid setting with adversarial ordering, feasibility forces the selection guarantee to α ≤ ½. Combined with the known construction that achieves ½, this pins the scheme at exactly ½ selectable. Every active item gets a 50% chance of acceptance, and no scheme of this form does better.

02 Projects

1. TRACE

   January 2026

   Explains why a stock moved

   A scoring model with eight factors, built on data from six financial APIs. It constructs and ranks causal graphs that explain a stock's price movement on a given day. FastAPI backend, React frontend, with results streamed to the browser as they are computed.

   • Python
   • FastAPI
   • React
   • Causal graphs
   • Streaming

   Visit tr4ce.net

2. Site Memory

   2026

   Chrome extension, published on the Chrome Web Store

   Saves your text highlights and notes on any web page or PDF, then restores them automatically the next time you visit. Highlights re-anchor themselves, so they survive changes to the page. Everything is stored on your own device. No accounts, no syncing, no tracking.

   • JavaScript
   • Chrome MV3
   • PDF.js
   • Local storage

   Chrome Web Store Source code

3. Google Drive Search Agent

   February 2026

   Answers questions about your documents

   An agent that searches Google Drive and answers questions about what it finds, across more than 10 file types. It runs a tool loop: search, open a file, read it, then repeat until it can answer. Caching the prompt and the tool results cut inference cost by about 90%, measured with an eval harness that scores each system prompt on token count and answer correctness.

   • Python
   • Anthropic API
   • Flask
   • OAuth
   • Prompt caching
   • Evals

   Source code

   Not hosted online. Reading a visitor's Drive needs Google's restricted scope verification, so the agent runs locally with your own credentials. Setup steps are in the README.

4. Do LLMs Sample Randomly?

   December 2025

   An experiment on how models pick numbers

   1,000 API calls testing whether a model gives a less biased number when asked to hide one inside a story, compared to asking for a number directly. Both methods fail a chi square test against a uniform distribution (p < 0.001), but the gap is large. Direct requests return 7 in 94.6% of samples, compared to 31.2% when the number is embedded in a story.

   • Python
   • Chi square test
   • Experiment design
   • Matplotlib

   Source code

03 Experience

1. Armatus Capital

   Software Engineering Intern, Agentic AI Infrastructure

   July 2026 to Present
   • Built and deployed a financial analytics platform with 555 automated tests. It turns daily market data for over 3,200 equities into six interactive tools used by a fund manager.
   • Built an AI research pipeline on top of LLM and SEC filing APIs. Every claim in a generated analysis is backed by a source citation that is verified automatically.
   • Cut false positives in a statistical market signal detector from 3.8 per day to 0.03 per day by rebuilding it around hypothesis testing.

2. University of Chicago

   Researcher (REU), Topological Dynamical Systems

   June to September 2026
   • Studying illumination problems in mathematical billiards and Veech surfaces under Dr. Tina Torkaman.

3. University of Chicago

   Researcher, Algorithmic Game Theory

   June to September 2025
   • Proved a tight optimality bound for online contention resolution schemes on rank 1 matroids, a framework used in auction design and online pricing under uncertainty.
   • Constructed a matching algorithm that achieves the bound, confirming that 50% acceptance probability is exactly optimal under adversarial ordering.

4. Maroon Capital

   Analyst, UChicago quantitative finance and trading club

   October 2025 to Present
   • Developed a systematic trading strategy that placed 1st out of 13 teams in the club competition.
   • Built a stock screener that uses regression on company fundamentals to flag potentially mispriced stocks.

5. University of Chicago

   Course Assistant, Calculus I to III

   September 2025 to Present
   • Grade weekly problem sets for over 60 students per quarter.

04 Background